[Deals like this tend to expire quickly so this article may be out of date after April 17, 2016]
Kudos to onemileatatime.boardingarea.com for finding this deal!

Various airlines are offering an excellent deal where you can fly for under $2,000 from the US to Europe.  These fares are available on several alliances including OneWorld (which can be credited to American Airlines).  American Airlines offers one of my favorite elite programs with perks that include complimentary first class upgrades and reasonable award flight redemption rates.  You can credit the flights below to American Airlines’s or Alaska Air’s frequent flier program.  In addition, you’ll want to use a credit card–such as the Chase Sapphire Preferred, Citi Prestige, or Citi Advantage Platinum–that offers additional points for airfare purchases.

I used Google Flights to find exact dates and organized the screen shots by departure city.  After you find the flight that you want, I recommend booking on Orbitz so you can earn Orbitz Rewards in addition to airline miles.

Departing New York 

• Airline: Iceland Air
• Destinations: Stockholm, Helsinki, Oslo, Copenhagen
• Dates: March 2016 to February 2017
• Special requirements: no requirements
• Other notes: Iceland Air allows free stopovers in Iceland.  In addition, you may be able to credit these flights to Alaska Airlines and likely earn both elite and redeemable miles for 150% of actual miles flown.

From Google Flights.  Google and the Google logo are registered trademarks of Google Inc., used with permission.

Departing Washington DC

• Airline: KLM, Iceland Air, Lufthansa, Turkish, United
• Destinations: Athens, Stockholm, Helsinki, Oslo, Copenhagen
• Dates: March 2016 to February 2017
• Special requirements: no requirements
• Other notes: Iceland Air allows free stopovers in Iceland.  In addition, you may be able to credit these flights to Alaska Airlines and likely earn both elite and redeemable miles for 150% of actual miles flown.  KLM flights can credit to Alaska Air and earn both elite and redeemable miles for 125% of actual miles flown.  KLM flights also credit to Delta and earn elite miles for 150% of actual miles flown and earn redeemable miles based on the cost of the fare and your Medallion status.

From Google Flights.  Google and the Google logo are registered trademarks of Google Inc., used with permission.

Departing Canada (Toronto)

• **I normally wouldn’t list Canadian cities, but the business class fares (under $1,700) are so good that it may be worth booking a separate positioning flight so you can fly out of Canada.
• Airline: SATA, Iceland Air, Air Transit ($1,000 to London), Finnair
• Destinations: too many to list
• Dates: March 2016 to February 2017
• Special requirements: no requirements
• Other notes: Iceland Air allows free stopovers in Iceland.  In addition, you may be able to credit these flights to Alaska Airlines and likely earn both elite and redeemable miles for 150% of actual miles flown.  KLM flights can credit to Alaska Air and earn both elite and redeemable miles for 125% of actual miles flown.  Finnair flights credit to American Airlines at the rate of 150% redeemable and elite (EQMs) of actual miles flown.

From Google Flights.  Google and the Google logo are registered trademarks of Google Inc., used with permission.